Davidsonian propositions page 1 Abstract of “Davidsonian Propositions” Donald Davidson understood utterances to be the fundamental truth-bearers, assigning no theoretical or explanatory role whatsoever to propositions. However, given that he held that most of what people say is true, he was committed to believing that there are such things as propositions. This essay constructs entities a Davidsonian can accept which fit his view of meaning. Propositions are sets of possible utterances. This reverses the order of theoretical explanation. Propositions are centered equivalence subsets of the relation “is correctly interpreted as” among utterances, akin to Carnap’s similarity circles. Such entities fit truisms about propositions and can be precisified to play many of the roles propositions play in philosophical theories, except that of being fundamental truth-bearers. Standard objections to such a linguistic reduction of propositions are shown to rest on mistakes. For instance, the objection propositions would be even if there were no speakers is akin to the fact that Aristotle might not have been called Aristotle, even though there could not be a situation in which “Aristotle is not called `Aristotle’” can be truly said.

Davidsonian propositions page 2 Davidsonian Propositions Davidson’s philosophy of language had no role for propositions to play in a theory of meaning. The basic truth-bearers are utterances1 in idiolects. However, by his principles of interpretation, Davidson was committed to the truism that there are such things as propositions, since otherwise no positive sentences using “proposition” would be true. Davidson denied that there are propositions in the philosophers’ sense. But Davidson would not want to say that, while “Galileo said that the Earth moves” is true, “Galileo stated the proposition that the Earth moves” is false. Propositions exist for Davidson, even though they play no explanatory or theoretical role in the theory of meaning. In the same way, a modern chemist denies that there is any such element as the earth which Aristotle and other ancients theorized about, while acknowledging that there are earthmoving machines. What the chemist denies is the associated theory—that earth is an element and something that stones and salt both are. The Davidsonian view this essay proposes is that propositions exist in the way earth does—as a more or less loose and vague kind of entity. The fundamental explanatory role of propositions has been to be the meanings of sentences. In philosophical theories, propositions are the fundamental truth-bearing entity, which utterances or uses of sentences in natural languages express. A proposition is what two sentences both express when the two sentences have the same meaning. To deny that there are propositions in this sense is to deny that there is any entity that fills that role. It is in this sense that Davidson denies that there are propositions. Davidson argues (1967) that the postulation of meanings as entities is useless in giving a theory of meaning for a natural language. He proposes that a theory of meaning is an account of how the truth-conditions of sentences can be grasped. In order to understand another’s utterances, one must be. able to produce a sentence of one’s own that is true if and only if the other’s sentence is true, for each sentence of the other’s language. Interpretation constructs such theories about another person’s language. A theory or a truth-definition is thus a counterfactualsupporting theory of the truth-conditions of a potential infinity of the other’s sentences.

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Under “utterance” I am including inscribings. There are some differences between inscriptions and utterances, but the connection to intentional production remains, even when inscriptions are copied. See (reference deleted for blind review).

Davidsonian propositions page 3 A Davidsonian account of propositions thus reverses the usual order of dependence. Rather than analyzing correct interpretation of a sentence as expressing the same proposition or meaning, and thus taking propositions to be theoretical objects which ground interpretations, a Davidsonian theory treats propositions as posits based on interpretation of utterances according to the guidelines of radical interpretation. The project of this essay is to describe and defend an account of propositions as constructions out of meaningful linguistic entities. The essay will argue that propositions are “things said” in the sense that Davidson explicates in his (1968). The Davidsonian view would seem obviously to be that whatever is indicated by the demonstrated utterance in his account of indirect discourse is exactly what propositions are, according to him. II Desiderata for an account of propositions: An account of what kind of posit propositions are should capture the truisms about propositions. Here are some of those truisms: 1) Every utterance with a truth-value should express a proposition. In neutral terms, there should be a function from utterances with truth-values to propositions. 2) Propositions should be entities that can be expressed in more than one language. 3) Propositions should be objects of propositional attitudes. 4) Propositional identity should be preserved by correct interpretation. If A is a correct interpretation of B, then the proposition expressed by A is the same as the proposition expressed by B. 5) Some propositions may be unexpressed by any actual utterance. III Davidsonian propositions a) The basic theory Davidson’s “On Saying That”(1968) set out a theory of indirect discourse that can be generalized to propositional attitudes of all sorts. He treats “Galileo said that the Earth is round” as having the form, “Galileo said that. The Earth is round.” The second full sentence is the utterance demonstrated by “that.”2 The object demonstrated is presented as the thing Galileo said. For Davidson’s English utterance to be the thing Galileo said, which was in fact something in Italian, it must say the same thing as Galileo’s utterance. Davidson proposes “samesaying” as

2

My preference is to take the fundamental linguistic items to be utterances rather than Interpreted Logical Forms. Individual utterances differ in, for instance, the intended referents of demonstratives.

Davidsonian propositions page 4 the relation that holds between the presented utterance and Galileo’s utterance when the presented utterance is a correct interpretation of what Galileo said. “Correctly interprets” for Davidson means “maximizes agreement in beliefs and desires” and so is compatible with there being two or more distinct and perhaps non-equivalent English sentences correctly interpreting Galileo’s utterance. Without meanings to provide the criterion for correct interpretation, it can happen that non-equivalent interpretations provide equally acceptable theories of the truth-conditions of a person’s utterances. Thus, “A is acceptably interpreted as B” is not quite the same as “A means the same as B.” For one thing, “is acceptably interpreted as” is not transitive. Since Davidson is constructing an account of meaning from peoples’ speech-actions, and action-interpretation is sometimes indeterminate, meaning is sometimes indeterminate. In brief, Davidsonian meaning across idiolects is vague in a way that metaphysical entities, such as Fregean senses, are not. A construction of propositions from this “correctly interprets” relation would dispense with meanings as entities. The “correctly interprets” relation is a perfectly good relation, as we argue below, that does not require an ontology of meanings as foundation. That is, just as a theory of length based on an operational definition of “is the same length as” can avoid postulating lengths as objects, so a theory of meaning need not quantify over meanings. In a sense, the maxims of action- and so speech-action interpretation give Davidson’s operational definition of “means the same as.” While Davidson’s paratactic theory has been attacked on many fronts, it has also been effectively defended.3 It is therefore worth considering as an alternative to accounts of propositions that treat them as entities grounding linguistic meaning. If we propose that propositions are things said in Davidson’s sense, we need to give some account of what sort of thing they are. Although no appeal to propositions is required in order to have an adequate account of propositional attitudes or a theory of meaning, we have to say something more to explicate sentences like “Every proposition he asserted had been discussed thoroughly by previous speakers,” and the like. If we quantify over propositions, they had better be something. In the same way, a theory of length that does not take lengths to be fundamental objects must provide something for the nominal to refer to. The obvious candidate would, of course, be a set of possible objects of the same length. Supposing such a definition of “length” based on some 3

See Rumfitt (1993) and Blair (2003).

Davidsonian propositions page 5 measuring operation, very few of the lengths in a Platonic ontology of lengths would actually be based on such measurements. The vast majority of lengths would not even be physically realizable. So, the reduction of lengths to “is that same length as” would be largely about possible measurements, in some mathematical sense of “possible.” Much the same will be true of the Davidsonian account of propositions based on correct interpretation. The obvious something for a proposition to be for a Davidsonian account of meaning is a class of things said or sayable connected by the “says the same as” relation. Two possible utterances A and B say the same thing, according to a standard, if each is an acceptable interpretation of the other, according to that standard. So, a first stab at what a proposition amounts to is an equivalence-class of same-saying utterances. This will not quite work, however, because “says the same as” is not in practice a transitive relation. In practice, as we will argue below, various standards for acceptable interpretation apply in various contexts, and many such standards would be loose enough so that transitivity would not be preserved. The standards for philosophical accounts of property-identity in philosophical theories of “property” as a technical term of metaphysics, such as “X expresses the same proposition as Y if and only if X is logically equivalent to/necessarily equivalent to/ intensionally isomorphic to/ synonymous with Y,” are indeed intended to be transitive relations. However, if our interest is in which sentences using “proposition” are true according to the truisms, not all standards are likely to be transitive. If the standard is “correctly interpreted as the same as” in Davidsonian terms, we should not expect transitivity at all.4 We are constructing an account of the English term “proposition,” not of the various technical precisifications of the term, even though many of those can be constructed by setting criteria, as we will see below. The project for a Davidsonian is to find something which matches the non-technical term “is a proposition.” In order to allow for the possibility that a relation defining “is the same proposition” could be non-transitive, even though “is the same proposition” is transitive, I propose the notion of a “equivalence subset” of a relation.5 Consider the relation “is no more than four larger than” as a relation among numbers, i.e. a set of ordered pairs. Suppose Fred’s utterance is item 3, and 4

Once again, an analogy with measurement-theory suggests itself. Suppose the operation for “is the same length as” is setting two objects next to one another. Then a chain of objects 1 through 1000000 such that object n comes out the same length as object n+1 by the test can easily be such that object 1 is not the same length as object 1000000. In the domain of micro-particles and the wave-lengths electrons dropping from one energy level to another, a criterion can preserve transitivity. Nothing like that is likely to be available for “means the same as.” Human conditions, unlike micro-particle conditions, are likely to be vague. 5 The notion proposed here is an adaptation of Carnap’s (1928, section 72) similarity circles.

Davidsonian propositions page 6 suppose that the distances between natural numbers parallels distances among utterances. Within the set {1,2,3,4,5}that relation is transitive. Every item in the set is no more than four larger than any other. So, the equivalence subset of the no more than four larger than relation centered on 3 is the 25-element set {, ,,,, , ,…., }. We can think of a proposition in the sense of “what Fred said” as such a equivalencesubset of possible utterances centered on Fred’s actual utterance. So, the proposition that Fred uttered would be the set of possible utterances in possible idiolects such that each element “says the same thing as” Fred’s utterance and each also “says the same thing as” any other element in the set. Many of the utterances that would be the same proposition as utterance 5 would not be the same proposition as utterance 3, since the equivalence subset centering on 5 would not include 3. That is, although 5 is no more than 4 different from 3, 8, which is no more than 4 different from 5, is more than 4 different from 3. So, while 3 and 8 are both in some equivalence subset defined on the “no more than 4 different from” relation which includes 5, there is no equivalence subset of which they are both members. So, “is the same proposition as” is an equivalence relation even though the relation on which it is based is not. “The same proposition as” relation, apart from the technical precisifications proposed by philosophers, has the same characteristic. “Acceptable interpretation” may be tolerated by the “same-saying” relation, relative to a standard, so that all of the pairs , , , and are each “acceptably interpreted” as the other, relative to that standard, while neither of the pair is acceptably interpreted as the other. Different standards for “saying the same thing” apply in different circumstances. Suppose Beatrice says to Bill, “You make me so mad I could kill you.” If Fred asks me what Beatrice said to Bill, I can say “She said she was furious with him” and be telling the truth. However, when Bill meets a bad end, Beatrice is a suspect, and I am on the witness stand, I am lying if I say anything other than something that conveys the exact words. I do this by saying “Beatrice said that Bill makes her so mad she could kill him,” with “Bill” replacing the pronoun “you” and a third person pronoun replacing “Beatrice.” The conditions for court-room reporting are roughly the identity-conditions philosophers propose for propositions as contents of beliefs. David Lewis (1986, page 49 and 185) observes that there are many things philosophers want meanings or propositions to do, and that various criteria for what it is for two expressions to express the same proposition are appropriate for different purposes. A similar kind of variety of

Davidsonian propositions page 7 conditions for “same thing said” obtain for indirect discourse. The kind of interest- and contextdependence of what it takes for an indirect discourse sentence to be true corresponds well with the variety of identity-conditions metaphysical theorists have proposed for propositions. The difference is that the philosophical accounts of propositions require precise criteria. For instance, someone needing propositions with the identity-conditions of sets of possible worlds can specify the condition for propositional identity as “metaphysically necessarily equivalent.” Unless one is a realist about possible worlds, little is lost in terms of reducing propositions to something else. Whether any conditions on utterances6 short of identity will provide an adequate criterion for identity of propositions as objects of every propositional attitude is questionable. Benson Mates’(1950) example of deeply imbedded occurrences of “Greek” and “Hellene” makes the point in one way. Kripke’s (1979) Pierre raises another difficulty. It may be indeterminate whether even two occurrences of the same non-indexical sentence express the same proposition. When Pythagoras and Dedekind both say “Two is the only even prime number” “number” has a different extension for Dedekind. If this kind of difference can yield different propositions, then two English speakers with different knowledge about dogs may not state the same proposition by “There are dogs.” The ultimate fine-grainedness, for a Davidsonian account of propositions, treats the equivalence-class centered on a given utterance as the unit set of the utterance itself. If propositions are objects of belief such that substitution in any context of whatsoever level of embedding preserves truth, then those are the propositions that are called for. A Davidsonian account of “proposition” is an account that accords with the theoryneutral truths about propositions that yield truisms. However, it is perfectly open to a theoretician to specify conditions for propositional identity suitable for particular philosophical purposes. Such technical terms can start with the ordinary notion and specify what the relation of “says the same as” will be. Typically the relation will be transitive, as, for instance, the identity relation and “metaphysically necessarily if and only if” are. That is, any condition one wishes can be used to define a subset of propositions as constructed above. No such theory need add ontology to the ontology already required in order to have sentences of a language.

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I ignore the intricacies of how many contextual parameters have to be inserted to determine a single proposition from a given context-dependent utterance. See Kaplan (1989) for a classic introduction to that topic.

Davidsonian propositions page 8 IV Meeting the desiderata The abstract objects constructed above are obviously not what an English speaker who has learned to use the term “proposition” has explicitly in mind. Generally, what kinds of objects are is learned, not by learning definitions, but by learning when to apply the term. Very few posited kinds of objects outside of mathematics or the special sciences are learned by learning definitions in other terms. For the special uses of “proposition” by philosophers, the above account makes it clear how to refine “proposition” for special technical purposes. These abstract objects constructed above are not less abstract than propositions as construed by other philosophers. Their virtue, from a Davidsonian point of view, is that they are constructions out of interpreted meaningful expressions, which expressions do not require propositions to supply meanings. They clearly meet the desiderata above. Whether they meet other desiderata is the subject of the next section. 1) Every utterance with a truth-value does indeed express a proposition. There is obviously, for every utterance with a truth-value, a set of possible utterances that correctly interpret that utterance, according to some standard. 2) Propositions as construed above are entities that can be expressed in more than one language, at least according to some standard of interpretation. On a fine-grained enough standard of property-identity, perhaps the equivalence-class will be just utterances in a single language. Perhaps what has been claimed about poetic meaning, that it cannot be transferred across linguistic borders, would be a counter-example. But this sort of counter-example would be a problem 3) Propositions as constructed above are based on the Davidsonian account of propositional attitudes. The Davidsonian idea is precisely that the “that” in “John believes that Alberta is a province” is a demonstrative pointing to “Alberta is a province” which gives the content of the belief. 4) Propositional identity should be preserved by correct interpretation. If A is a correct interpretation of B, then the proposition expressed by A is the same as the proposition expressed by B. As noted above, “correct interpretation” varies with circumstances in much the way that various identity-conditions proposed for propositions by different philosophical theories. The difference, of course, is that for every philosophical theory, since “proposition” is a technical term, the chosen version of the relation “A is a correct interpretation of B” is transitive.

Davidsonian propositions page 9 5) Some propositions may be unexpressed by any actual utterance. Davidsonian propositions are abstract objects. For anyone, the sentences of an idiolect are by and large merely possible, since only an infinitesimal fraction of the sentences generated by a syntax are actually produced. Corresponding to each sentence are many possible utterances. So, sentences and possible utterances themselves are abstract objects, and propositions are sets of such abstract objects. As we will see below, the cardinality of the population of propositions so construed is very large indeed. V Objections and Replies It should be quite apparent that the proposed account of propositions is a variant of reductive accounts of propositions and other entities that treat them as constructions out of linguistic items.7 The present account must therefore address a variety of traditional objections to linguistic reductions. a) Objection 1: Propositions are true or false independently of the existence of language-users. Suppose that language-users had never come into existence. In that circumstance, it would have been true that there are no sentences. That is, the proposition that there are no sentences would have been true. But there would not exist sentences to have truth-values. So, the proposition that there are no sentences could not be a construct out of sentences. So, propositions rather than sentences must be the truth-bearers and exist independently of whether sentences do. Reply: This puzzle is of the same sort as puzzles about how it can be true that Aristotle might not have been called “Aristotle.” There are no possible worlds in which speakers can truly say “Aristotle is not named `Aristotle.’” Nevertheless, there are worlds in which “Aristotle is not named `Aristotle’” is true. “Aristotle is not named `Aristotle’” is true in those worlds even though that utterance or inscription, interpreted from the point of view of that world, with the references for terms obtaining in that world, would not be true. The utterance is stated in this world and is to be interpreted with this world’s references. So, the utterance is true in that world. In the same way, while there are no worlds in which “There are no language-users” can be truly uttered, there are worlds in which that sentence, a sentence of ours, is true. The question is not what truth-values our sentences would have if those sentences were in other worlds. Rather, our this-worldly sentences are evaluated at other worlds.

7

Obviously, a Davidsonian would propose analogous accounts of properties (constructed out of open rather than closed sentences) and facts (construed as states of the world at large that it is such that a given sentence is true)is.

Davidsonian propositions page 10 A variant of this objection cites situation in the distant past, before there were languageusers, and therefore before there were sentences. In the distant past there were no speakers saying “Stars are just beginning to form” but my inscription or utterance, “Stars are just beginning to form” was true. We evaluate our utterance relative to another, no-longer-present time. At that time, this sentence of mine was true. If there had been someone around to utter it, an utterance of that sentence would have been true. As it happens, my utterance produced now was true then. Objection 2: There are more propositions than there are things people have said. Reply: This does not mean that there are more propositions than there are sentences. On the present theory, every possible sentential utterance-type expresses a proposition. Possible utterance-types are abstract objects of a familiar sort, the sentences generated by the syntax of an idiolect. It is easy to come up with sentences and so propositions that have never been expressed. A syntax, coupled with a recursive semantics, will, after a few iterations of a familiar construction, produce sentences, i.e. possible utterances, that have never been uttered, certainly not by someone speaking your idiolect. A truth-definition for an idiolect, giving the meaning of every sentence in that idiolect, generates what the truth-conditions of an infinity of utterances would be. Truth-definitions support counterfactuals. Objection 3: Expressions of a language are enumerable, but the true propositions are not. Consider any real number, say pi. For every other real number n, either it is greater than pi or smaller than pi. In general, \/n\/m (n≠m -> (n>m v n